An Introduction to the Mathematical Theory of Inverse Problems (Paperback)

Andreas Kirsch

ISBN 10: 1461428513 / ISBN 13: 9781461428510

Published by Springer-Verlag New York Inc., New York, NY, 2013

About this Item

Paperback. This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed.In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781461428510

Bibliographic Details

• Title: An Introduction to the Mathematical Theory of Inverse Problems (Paperback)
• Publisher: Springer-Verlag New York Inc., New York, NY
• Publication Date: 2013
• Language: English
• ISBN 10: 1461428513
• ISBN 13: 9781461428510
• Binding: Paperback
• Edition: 2nd Edition
• Condition: new

About this title

Synopsis

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.
The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.
The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed.

In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.

About the Author

Andreas Kirsch is a Professor in the Department of Mathematics at Karlsruhe Institute of Technology.